The governing equations of the propagation of solitary waves are reformulated in two?dimensional microstructures solids through the Mindlin theory. And by using the traveling wave transformation, the complicated nonlinear partial differential equations are then simplified to a nonlinear ordinary differential equation. Finally, using the qualitative analysis theory of the dynamical systems, the existence conditions and geometrical characteristics of the solitary waves in two?dimensional microstructure solids were analyzed. They can form an asymmetric solitary wave in the two?dimensional microstructure solids, when the medium parameters satisfy certain appropriate conditions.